5 8 Applying Special Right Triangles Warm Up

5 -8 Applying Special Right Triangles Warm Up For Exercises 1 and 2, find the value of x. Give your answer in simplest radical form. 1. 2. Simplify each expression. 3. Holt Geometry 4.

5 -8 Applying Special Right Triangles Holt Geometry

5 -8 Applying Special Right Triangles Holt Geometry

5 -8 Applying Special Right Triangles Example 1 A: Finding Side Lengths in a 45°- 45º- 90º Triangle Find the value of x. Give your answer in simplest radical form. By the Triangle Sum Theorem, the measure of the third angle in the triangle is 45°. So it is a 45°-45° 90° triangle with a leg length of 8. Holt Geometry

5 -8 Applying Special Right Triangles Example 1 B: Finding Side Lengths in a 45º- 90º Triangle Find the value of x. Give your answer in simplest radical form. The triangle is an isosceles right triangle, which is a 45°-90° triangle. The length of the hypotenuse is 5. Rationalize the denominator. Holt Geometry

5 -8 Applying Special Right Triangles Add to a Separate Sheet of Paper Holt Geometry

5 -8 Applying Special Right Triangles Holt Geometry

5 -8 Applying Special Right Triangles Holt Geometry

5 -8 Applying Special Right Triangles Holt Geometry

5 -8 Applying Special Right Triangles Example 3 A: Finding Side Lengths in a 30º-60º-90º Triangle Find the values of x and y. Give your answers in simplest radical form. 22 = 2 x Hypotenuse = 2(shorter leg) 11 = x Divide both sides by 2. Substitute 11 for x. Holt Geometry

5 -8 Applying Special Right Triangles Check It Out! Example 3 a Find the values of x and y. Give your answers in simplest radical form. Hypotenuse = 2(shorter leg) Divide both sides by 2. y = 27 Holt Geometry Substitute for x.

5 -8 Applying Special Right Triangles Holt Geometry

5 -8 Applying Special Right Triangles Holt Geometry

5 -8 Applying Special Right Triangles Holt Geometry

5 -8 Applying Special Right Triangles Lesson Quiz: Part I Find the values of the variables. Give your answers in simplest radical form. 1. 2. x = 10; y = 20 3. Holt Geometry 4.

5 -8 Applying Special Right Triangles Lesson Quiz: Part II Find the perimeter and area of each figure. Give your answers in simplest radical form. 5. a square with diagonal length 20 cm 6. an equilateral triangle with height 24 in. Holt Geometry

5 -8 Applying Special Right Triangles Warm-Up Find the values of the variables. Give your answers in simplest radical form. 1. 2. x = 10; y = 20 3. Holt Geometry 4.